本文選題：分?jǐn)?shù)階差分方程 + 邊值問題��； 參考：《西北師范大學(xué)》2013年碩士論文

【摘要】：本文運(yùn)用錐上的不動(dòng)點(diǎn)理論,研究了幾類分?jǐn)?shù)階差分方程邊值問題解的存在性. 全文共分為三章. 第一章運(yùn)用錐拉伸與壓縮不動(dòng)點(diǎn)定理和Brouwer定理,研究了分?jǐn)?shù)階差分方程三點(diǎn)邊值問題 -△~νy(t)=f(t+ν-1, y(t+ν-1)), t∈[0, b]N_0(P1) y(ν-2)=0, y(ν+b)=αy(η)解的存在性.其中f:[ν1,ν+b1]Nν1×R→R+為連續(xù)函數(shù), b,η∈N,ν2η ν+b,1ν 2, α0.當(dāng)非線性項(xiàng)f滿足一定條件時(shí),建立了上述問題解的存在性定理. 第二章運(yùn)用錐拉伸與壓縮不動(dòng)點(diǎn)定理,研究了一類分?jǐn)?shù)階差分方程邊值問題 -△~νy(t)=λf(t+ν-1, y(t+ν-1)), y(ν-2)=g1(y),(P2) y(ν+b)=g2(y)正解的存在性,其中f:[ν-1,ν+b-1]N_(ν-1)×[0,∞)→[0,∞)是連續(xù)函數(shù),g1, g2∈C([ν-2, ν+b]N_(ν-2),[0,∞))是已知函數(shù)且1ν≤2.通過計(jì)算出上述問題的Green函數(shù),從而給出這個(gè)問題解的和分表達(dá)式,進(jìn)而結(jié)合錐拉伸與壓縮不動(dòng)點(diǎn)定理,得到邊值問題(P2)至少存在一個(gè)正解的充分條件. 第三章運(yùn)用Banach壓縮映像原理,研究了帶有分?jǐn)?shù)邊界條件的分?jǐn)?shù)階差分方程邊值問題解的存在性.其中t∈{0,1,...,b+1}, f:{ν1,ν,...,ν+b}×R→R是連續(xù)函數(shù),g∈C({ν-1, ν,..., ν+b}, R)是一給定函數(shù),并且1ν≤2,0≤α 1, α, ν∈R.當(dāng)非線性項(xiàng)f滿足一定條件時(shí),建立了上述問題解及正解的存在性定理.
[Abstract]:In this paper, by using the fixed point theory on a cone, we study the existence of solutions to boundary value problems for several kinds of fractional difference equations. The full text is divided into three chapters. In chapter 1, the three-point boundary value problem of fractional difference equation is studied by using the fixed point theorem and Brouwer theorem of cone stretching and squeezing. Y(t)=f(t-1, yt y(t)=f(t-1 n, t 鈭，

本文編號：1870493